Continuity and completeness of strongly independent preorders

David McCarthy*, Kalle Mikkola

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

We show that a strongly independent preorder on a possibly infinite dimensional convex set that satisfies two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfies two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii) mixture continuity; and (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided, illustrating the relevance of infinite dimensionality. (C) 2018 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)141-145
Number of pages5
JournalMATHEMATICAL SOCIAL SCIENCES
Volume93
DOIs
Publication statusPublished - May 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • MULTI-UTILITY REPRESENTATIONS
  • INCOMPLETE PREFERENCES
  • EXPECTED UTILITY

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